An enzyme which ligates something. The term is almost always used to refer to an enzyme that ligates DNA. There are many, many different ligases.
Basically, a DNA ligase is the opposite of a DNA endonuclease (sometimes referred to as a restriction enzyme). Ligase catalyzes the formation of the phosphate bond which links each nucleotide to each other in a DNA molecule.
Practically, DNA ligase is used to connect two pieces of DNA together. T4 ligase, the most widely used in modern biology, covalently links double stranded DNA molecules that have complementary ends.
Though massively useful for molecular biology, ligases evolved for other purposes. A number of ligases exist in mammalian cells that take part in DNA repair and replication.